%0 Journal Article %T Controlled diffusion processes %A Vivek S. Borkar %J Mathematics %D 2005 %I arXiv %R 10.1214/154957805100000131 %X This article gives an overview of the developments in controlled diffusion processes, emphasizing key results regarding existence of optimal controls and their characterization via dynamic programming for a variety of cost criteria and structural assumptions. Stochastic maximum principle and control under partial observations (equivalently, control of nonlinear filters) are also discussed. Several other related topics are briefly sketched. %U http://arxiv.org/abs/math/0511077v2